Right triangle ABC has a right angle at vertex C. The measures of the legs are: AC = x+2 BC= 2 AB: x+8 Find the length of AC
After making my sketch it was clear that:
(x+8)^2 = (x+2)^2 + 2^2
expand and you will see that the x^2 drops out and you can easily for for x
then find AC = x+2 = ....
To find the length of AC, you need to know the value of x. From the given information, we know that AC = x + 2.
To find the value of x, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (AB) is equal to the sum of the squares of the lengths of the legs (AC and BC). In equation form, it is written as:
AB^2 = AC^2 + BC^2
Substituting the given lengths, we have:
(x+8)^2 = (x+2)^2 + (2)^2
Expanding both sides, we get:
x^2 + 16x + 64 = x^2 + 4x + 4 + 4
Simplifying the equation, we get:
16x + 60 = 0
Now, let's solve for x:
16x = -60
x = -60/16
x = -3.75
Since length cannot be negative, we discard the negative solution. Therefore, x = -3.75 is not a valid solution for this problem.
As there seems to be an issue with the given values, I'm unable to proceed further to find the length of AC. Please recheck the measurements or provide additional information if possible.